I spoke with both Schlage and Nexia regarding this issue, (we get a number of questions regarding the BE-369) and to directly answer your question, both Schlage and Nexia reported that while it is possible to update the firmware of a BE-469 lock through the method you mentioned, you cannot update the firmware of the BE-369.
Now, this was stated by two supervisors, one at either support center. This appears to be the opposite of what you were informed, so it is difficult to reconcile, of course, but I have to take them at face value.
At this time, I do not personally recommend this model of lock for anything other than a Nexia system (and I cannot speak to its functionality with that system as we do not support Nexia, I just assume it has few issues as it is designed and packaged for use with it.) Alarm.com is working on the integration issues with this model, and I will request an update as to that process, but a large part of the problem may be (given what I was told by the support supervisors) a widely varying group of firmwares with no recourse for upgrading other than buying a new lock.
All that said, one bit of troubleshooting advice that the support centers offered directly was that since the unit operates on both AA and 9v batteries, if one of them is low, (particularly the AA, they mentioned) then the Zwave functionality would see issues as the module may be under-powered. This may be rather obvious and silly, but worth a look.